Print your own minis.
Gnome Stew has lovely print-and-fold minis in 1x1 and 2x2 inch dimensions. You can use any image you like to get customized minis quick.
Laminate a grid
Professional maps are often rigid and easily marked up--a Chessex board is quickly ruined by the wrong marker, and I'm guessing with a 6-year-old playing that's more of a certainty than a likelihood. Laminated maps, however, are a lot more forgiving.
You can use 1x1'' grid paper, or draw your own grid on butcher's paper or newsprint (if you've got a local newspaper printer, they often give away the endrolls for free). Then laminate it at a copy shop.
Use wet-erase markers or (my preference) Crayola washable window markers. Window markers come in more colors than wet-erase markers, don't smudge as easily, and actually wipe off more cleanly. If you accidentally use a dry-erase marker or sharpie on the laminate, mild cleaners and elbow grease usually get 'em off.
The D&DI is a great resource.
You'll be able to download every D&D 4e Dungeon and Dragon magazine, by issue or by article, which includes enough adventures to run at least three 1-to-30 campaigns. It'll also give you a searchable compendium of all mechanics and mechanical elements from every official publication (books, magazines, adventures) and comprehensive character- and monster-building tools.